Graded persistence diagrams and persistence landscapes

We introduce a refinement of the persistence diagram, the graded persistence diagram. It is the Mobius inversion of the graded rank function, which is obtained from the rank function using the unary numeral system. Both persistence diagrams and graded persistence diagrams are integer-valued functions on the Cartesian plane. Whereas the persistence diagram takes non-negative values, the graded persistence diagram takes values of 0, 1, or -1. The sum of the graded persistence diagrams is the persistence diagram. We show that the positive and negative points in the k-th graded persistence diagram correspond to the local maxima and minima, respectively, of the k-th persistence landscape. We prove a stability theorem for graded persistence diagrams: the 1-Wasserstein distance between k-th graded persistence diagrams is bounded by twice the 1-Wasserstein distance between the corresponding persistence diagrams, and this bound is attained. In the other direction, the 1-Wasserstein distance is a lower bound for the sum of the 1-Wasserstein distances between the k-th graded persistence diagrams. In fact, the 1-Wasserstein distance for graded persistence diagrams is more discriminative than the 1-Wasserstein distance for the corresponding persistence diagrams.Comment: accepted for publication in Discrete and Computational Geometr

The design and evolution of the beta two-stage-to-orbit horizontal takeoff and landing launch system

The Beta launch system was originally conceived in 1986 as a horizontal takeoff and landing, fully reusable, two-stage-to-orbit, manned launch vehicle to replace the Shuttle. It was to be capable of delivering a 50,000 lb. payload to low polar orbit. The booster propulsion system consisted of JP fueled turbojets and LH fueled ramjets mounted in pods in an over/under arrangement, and a single LOX/LH fueled SSME rocket. The second stage orbiter, which staged at Mach 8, was powered by an SSME rocket. A major goal was to develop a vehicle design consistent with near term technology. The vehicle design was completed with a GLOW of approximately 2,000,000 lbs. All design goals were met. Since then, interest has shifted to the 10,000 lbs. to low polar orbit payload class. The original Beta was down-sized to meet this payload class. The GLOW of the down-sized vehicle was approximately 1,000,000 lbs. The booster was converted to exclusively air-breathing operation. Because the booster depends on conventional air-breathing propulsion only, the staging Mach number was reduced to 5.5. The orbiter remains an SSME rocket-powered stage

REGIONAL GAINS AND LOSSES FOR CONSUMERS AND PRODUCERS FROM CHANGES IN FLUID MILK PRICES

Agribusiness,

Attractive internal wave patterns

This paper gives background information for the fluid dynamics video on internal wave motion in a trapezoidal tank.Comment: 2 pg, movie at two resolutions _low(Low-resolution) and _hr(High-resolution

Attractive internal wave patterns

This paper gives background information for the fluid dynamics video on internal wave motion in a trapezoidal tank.Comment: 2 pg, movie at two resolutions _low(Low-resolution) and _hr(High-resolution

Observation of Fano-Resonances in Single-Wall Carbon Nanotubes

We have explored the low-temperature linear and non-linear electrical conductance $G$ of metallic carbon nanotubes (CNTs), which were grown by the chemical-vapor deposition method. The high transparency of the contacts allows to study these two-terminal devices in the high conductance regime. We observe the expected four-fold shell pattern together with Kondo physics at intermediate transparency {G\alt 2e^2/h} and a transition to the open regime in which the maximum conductance is doubled and bound by $G_{max}=4e^2/h$. In the high-$G$ regime, at the transition from a quantum dot to a weak link, the CNT levels are strongly broadened. Nonetheless, sharp resonances appear superimposed on the background which varies slowly with gate voltage. The resonances are identified by their lineshape as Fano resonances. The origin of Fano resonances is discussed along the modelling.Comment: pdf including figures, see: http://www.unibas.ch/phys-meso/Research/Papers/2004/Fano-CVD-SWNT.pd